Chapter 5: Q5.69 (page 535)

For function $f (x) = x - 5 a n d g (x) = x^{2} - 2 x + 3, F i n d (a) (f . g) (x) (b) (f . g) (2)$

Short Answer

Expert verified

$(a) M u l t i p l y t h e g i v e n b i n o m i a l f u n c t i o n (f . g) (x) = (x - 5) (x^{2} - 2 x + 3) = x^{3} - 7 x^{2} + 13 x - 15 (b) M u l t i p l y t h e g i v e n b i n o m i a l f u n c t i o n (f . g) (2) = (x - 5) (x^{2} - 2 x + 3) = (2 - 5) (2^{2} - 2 \times 2 + 3) = - 9$

Step by step solution

Step 1

Given information:

$f (x) = x - 5 a n d g (x) = x^{2} - 2 x + 3$

Step 2

Multiplying polynomials require only three steps.

First, multiply each term in one polynomial by each term in the other polynomial using the distributive law.
Add the powers of the same variables using the exponent rule.
Then, simplify the resulting polynomial by adding or subtracting the like terms.

Step 3Part(a) Step1. Multiply the Polynomials

$p a r t (a) S t e p 1 . M u l t i p l y t h e p o l y n o m i a l s (a) (f . g) (x) = f (x) . g (x) S u b t i t u t e f o r f (x) a n d g (x) (f . g) (x) = (x - 5) (x^{2} - 2 x + 3) M u l t i p l y t h e p o l y n o m i a l s (f . g) (x) = x (x^{2} - 2 x + 5) - 5 (x^{2} - 2 x + 3) D i s t r i b u t e (f . g) (x) = x^{3} - 2 x^{2} + 5 x - 5 x^{2} + 10 x - 15 C o m b i n e l i k e t e r m s (f . g) (x) = x^{3} - 7 x^{2} + 15 x - 15$

Part(b) Step1. Multiply the Polynomials

$(b) I n p a r t (a) w e f o u n d (f . g) (x) a n d n o w a s k e d t o f i n d (f . g) (2) (f . g) (x) = x^{3} - 7 x^{2} + 15 x - 15 t o f i n d (f . g) (2) s u b t i t u t e x = 2 (f . g) (2) = {(2)}^{3} - 7 {(2)}^{2} + 15 (2) - 15 (f . g) (2) = 8 - 28 + 30 - 15 (f . g) (2) = - 5$

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For function $f (x) = x - 5 a n d g (x) = x^{2} - 2 x + 3, F i n d (a) (f . g) (x) (b) (f . g) (2)$

Short Answer

Step by step solution

Step 1

Step 2

Step 3Part(a) Step1. Multiply the Polynomials

Part(b) Step1. Multiply the Polynomials

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For functionf(x)=x-5andg(x)=x2-2x+3,Find(a)(f.g)(x)(b)(f.g)(2)

Short Answer

Step by step solution

Step 1

Step 2

Step 3Part(a) Step1. Multiply the Polynomials

Part(b) Step1. Multiply the Polynomials

One App. One Place for Learning.

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For function $f (x) = x - 5 a n d g (x) = x^{2} - 2 x + 3, F i n d (a) (f . g) (x) (b) (f . g) (2)$